I see my guess was wrong. The graph is a parabola not an ellipse.
And the equation is undefined when theta = 90 degrees.
Is it correct to say that no polar point appears when the ray is 90 degrees?
Let the focal point F be at the origin, the horizontal line
y = −2 be the directrix, and P = (r; θ) be equidistant from
the focus and the directrix. Using the polar variables r and θ,
write an equation that says that the distance from P to the
directrix equals the distance from P to F. The configuration of
all such P is a familiar curve; make a rough sketch of it. Then
rearrange your equation so that it becomes r = 2/1 − sin θ,
On which polar ray does no point appear?
I think this should be an ellipse.
But I am not sure what the last part of the problem is asking.